Problem #PRU-78130

Problems Set theory and logic Theory of algotithms Game theory Game theory (other) Algebra and arithmetic Algebraic equations and systems of equations Systems of linear equations
 12–14  3.0

Problem

There is a system of equations \[\begin{aligned} * x + * y + * z &= 0,\\ * x + * y + * z &= 0,\\ * x + * y + * z &= 0. \end{aligned}\] Two people alternately enter a number instead of a star. Prove that the player that goes first can always ensure that the system has a non-zero solution.